How do I show a rendered image in a new viewport without the verticies being highlighted?
I'm not sure if it is the ideal fix, but if you just want to not see the vertices in the view on the left (which show up because toggling into Edit Mode on that object is affecting its mode in both views), I think turning off Overlays in the left-hand-side view will give you what you want. I've indicated where the relevant button is below, and give an example of what the result looks like:



As alternative, there may also be a way to only switch mode on an object in one viewport window but not in another, but that I am not sure about.